In the beginning of the year 1611, Galileo supposed that he found in the eclipses of Jupiter’s satellites a simple and rigorous solution of the famous problem of the longitude, and attempts to introduce the new method on board the numerous vessels of Spain and Holland at once began.  They failed because the necessary observations required powerful telescopes, which could not be employed on a tossing ship.  Even the expectations of the serviceability of Galileo’s methods for land calculations proved premature.  The movements of the satellites of Jupiter are far less simple than the immortal Italian supposed them to be.  The labors of three more generations of astronomers and mathematicians were needed to determine them, and the mathematical genius of Laplace was needed to complete their labors.  At the present day the nautical ephemerides contain, several years in advance, the indications of the times of the eclipses and reappearances of Jupiter’s satellites.  Calculation is as precise as direct observation.

Influenced by an exaggerated deference, modesty, timidity, France in the eighteenth century surrendered to England the exclusive privilege of constructing her astronomical instruments.  Thus, when Herschel was prosecuting his beautiful observations on the other side of the Channel, we had not even the means of verifying them.  Fortunately for the scientific honor of our country, mathematical analysis also is a powerful instrument.  The great Laplace, from the retirement of his study, foresaw, and accurately predicted in advance, what the excellent astronomer of Windsor would soon behold with the largest telescopes existing.  When, in 1610, Galileo directed toward Saturn a lens of very low power which he had just constructed with his own hands, although he perceived that the planet was not a globe, he could not ascertain its real form.  The expression “tri-corporate,” by which the illustrious Florentine designated the appearance of the planet, even implied a totally erroneous idea of its structure.  At the present day every one knows that Saturn consists of a globe about nine hundred times greater than the earth, and of a ring.  This ring does not touch the ball of the planet, being everywhere removed from it to a distance of twenty thousand (English) miles.  Observation indicates the breadth of the ring to be fifty-four thousand miles.  The thickness certainly does not exceed two hundred and fifty miles.  With the exception of a black streak which divides the ring throughout its whole contour into two parts of unequal breadth and of different brightness, this strange colossal bridge without foundations had never offered to the most experienced or skillful observers either spot or protuberance adapted for deciding whether it was immovable or endowed with a motion of rotation.  Laplace considered it to be very improbable, if the ring was stationary, that its constituent parts should be capable of resisting by mere cohesion the continual